Key Features (1)
Key Features (2)
Exponential Growth Or Decay
Growth and Decay Models
Compound Interest
100
What is the initial amount for the function f(x)=2(3)x
initial amount=2
100
Adding or subtracting a number from x in an exponential function shifts the graph ______.
Left or right
100
How do you know if an exponential function represents decay?
If b is between 0 and 1
or simply b<1
100
A car's value can be modeled by the equation y=25575(0.65)^t, where y is the value of the car and t is the time in years.
How much is the car worth in 3 years?
$7023.53
100
How do you turn 7% into a decimal?
What is the given decimal of 7%?
7/100= .07
or you move the decimal two places to the left of 7 to get .07.
200
What is the y-int of the function below? 
(0,1)
200
What determines whether an equation will have a vertical stretch or vertical compression?
Ignoring the sign,when a>1 there is a vertical stretch. When a<1 there is a vertical compression. When a=1, there is no change.
200
What type of factor (growth or decay) does the equation
y=-2(2/3)^x
have? What is the factor?
Decay factor; 2/3
200
You bought $2000 worth of stocks in 2012. The value of the stocks has been decreasing by 10% each year.
Is this growth or decay, and what is the "b" value?
Decay, b=0.9
200
Ms. Wiggins deposited $1,000 in a CD at a 7% interest compounded quarterly for 5 years. How would you represent this scenario using the correct model?
y=1000(1+\frac{.07}{4})^{4*5}
300
If
f(x)=2/5(2)^x-4
what is f(4)?
2.4
300
What transformations have occurred from the parent function
y=(1/2)^x
to the new function
y = (1/2)^(x-1) + 2
shift right 1 and up 2
300
f(x)=a(1.07)x
Does this functions represent exponential growth or decay?
Exponential Growth
300
Annual sales of a fast food restaurant are $530,000 and increasing at a rate of 5%. What will the annual sales be in 6 years?
A=P(1+r)n
530000(1.05)6
=$710,250 or =$710,251
300
How much money would be in an account if $3500 is invested at a rate of 2% for 5 years, compounded continuously.
$3868.10
400
The variable b in an exponential function can be called_______.
hint: recall y=a(b)^x
Base, common ratio, Growth/Decay factor
400
What is the equation for the asymptote of the equation?
f(x)=2/5(2)^x-4
y=-4
400
Does the graph represent exponential growth or decay?
Exponential Growth
400
The yearly profits of a company at the end of 2020 was $25,000. The profits have been decreasing by 16% per year.
If this rate continues, in what year will the yearly profits drop below $5000?
In 2030.
(At the end of 2029, the profits are $5205.40 and at the end of 2030, the profits are $4372.50)
400
A thousand dollars is left in a bank savings account drawing 7% interest for 10 years. How much more money will you make if it is compounded monthly instead of quarterly?
$8.06
500
What's the value of b?
b = 2
500
State all differences of the equation
f(x)=-2(3)^{x+1}
Reflection across the x axis, vertical stretch, shift left 1
500
Consider the function below. What is the percent decrease?
f(x)=200(.73)^x
27%
500
In a certain forest, there are 20 rabbits. They are increasing at a rate of 20% per year.
In the same forest, there are 40 wolves. They are decreasing at a rate of 5% per year.
After how many years will there be about the same number of rabbits and wolves?
In 3 years, there will be 34 rabbits and 34 wolves.
500
What principal will amount to $3500 if invested at 4% interest compounded quarterly for 5 years?
$2868.41